A Representation Theorem and Applications

We introduce a set of transformations on the set of all probability distributions over a finite state space, and show that these transformations are the only ones that preserve certain elementary probabilistic relationships. This result provides a new perspective on a variety of probabilistic inference problems in which invariance considerations play a role. Two particular applications we consider in this paper are the development of an equivariance-based approach to the problem of measure selection, and a new justification for Haldane’s prior as the distribution that encodes prior ignorance about the parameter of a multinomial distribution.

• Type: Conference
• Year: 2003
• Where: ECSQARU
• Authors: Manfred Jaeger
• Keywords: ECSQARU 2003, Elementary Probabilistic Relationships, Probabilistic Inference Problems, finite State Space